To employ the QCB, one makes use of a two-sided measurement. The first
is on \(\mathcal {S}\) , putting it into its pointer states (i.e., \(\chi (\hat{\Pi }_{\mathcal {S}} :\mathcal {F})\)  now
provides the mutual information between \(\mathcal {S}\)  and \(\mathcal {F}\) ). This reflects
the action of \(\mathcal {E}/\mathcal {F}\)  and is the good decoherence limit—i.e.,
\({^{\sharp }}\hspace{-1.42262pt}\mathcal {E}\rightarrow \infty \)  provided \(\mathcal {S}\)  and \(\mathcal {E}\)  have interacted for some
finite time under the evolution given by Eq. (REF ) and Eq.
(REF ) This also requires that the coupling strength to the environment components
do not depend on \({^{\sharp }}\hspace{-1.42262pt}\mathcal {E}\) .. The second is on \(\mathcal {F}\)  to access the pointer state. By Fano's inequality
[1]}, [2]},
\(\chi (\hat{\Pi }_{\mathcal {S}} :\mathcal {F})\ge I_{\mathrm {acc}}\left(\hat{\Pi }_{\mathcal {S}}\right)\ge H_{\mathcal {S}}-h\left(P_{e}\right)-P_{e}\ln \left[D-1\right],\) 
